The Encounter of Geometry with Learning

Luis Moreno-Armella
Rubén Elizondo Ramírez

Abstract: Conceiving of space as the space around us, and the inflexibility of
Euclidean geometry to analyze physical space for over 20 centuries led to a crisis
in the conception of mathematics. Eventually this created a tension between
cognition and logic. We explain how such developments challenge learning
paradigms and mathematical inquiry for learners today. We introduce this epistemological
analysis to help us think about the nature of mathematical knowledge
and hence learning today. The direct correspondence between physical
space and mathematical structure was broken after the discovery of non-Euclidean
geometry. Similarly, this is what is occurring with the implementation of
dynamic mathematical environments that breaks the correspondence with static
mathematical objects.
With our digital model of non-Euclidean geometry we focus on the affordances
of new technological environments and the knowing of mathematics
learners. This illustrates a representational re-description of mathematics and
how it can modify our natural ontology to accommodate change and

Keywords: epistemology, model, representation, intuition, learning.


DOI: 10.24844/EM2901.01



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